I thought with songs like “Come Together”, “Don’t Let Me Down”, “Revolution” (the fast version), “I Want You (She’s So Heavy)”, and “Yer Blues”, Lennon was making a strong move toward, if not Heavy Rock, at least Progressive Rock.
But they did do heavy music. Helter Skelter and Revolution are as raw as the Stooges. The Op didn’t say the Beatles put out a speed metal album. He didn’t say a Rap album, etc. the Beatles couldn’t have done either. The did make a little heavy music and I think they could have done a good heavy album.
The OP mentioned Helter Skelter as being on an album, and being the lightest track. I believe that order was beyond the musical ken of Lennon and McCartney. So to answer the OP, not only do I believe it wouldn’t have been received well by critics and/or fans, I don’t believe they could have sustained the level of quality they were known for and rocked “heavily” for a full LP.